MA302 Grantham Week 3 Calculus Functions and Graphs Practice Paper Assignment Submission For this assignment, you submit answers by question parts. The nu

MA302 Grantham Week 3 Calculus Functions and Graphs Practice Paper Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

Consider the following function and graph.f(x) = 3

x
x2 ? 9

Determine whether f(x) approaches ? or -? as x approaches 3 from the left and from the right.
(a) lim x?3? f(x)

(b)

lim x?3+ f(x)

2.–/11 pointsLarCalc11 1.5.011.
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My Notes

Consider the following function.f(x) =

1
x2 ? 16
Complete the following table. (Round your answers to two decimal places.)
x

?4.5

?4.1

?4.01

?4.001

?4

?3.999

?3.99

?3.9

?3.5

f(x)

?

Use the table to determine whether f(x) approaches ? or ?? as x approaches

?4

from the left and from the right.

lim x??4? f(x) =

lim x??4+ f(x) =

Use a graphing utility to graph the function to confirm your answer.

3.–/1 pointsLarCalc11 1.5.040.
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My Notes

Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim x ? (?1/2)+

6×2 + x ? 1
10×2 ? 5x ? 5

4.–/1 pointsLarCalc11 1.5.041.
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My Notes

Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.)lim x?0?

6 +
5
x

5.–/1 pointsLarCalc11 1.5.046.
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My Notes

Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim x ? (?/2)+

?8
cos x

6.–/1 pointsLarCalc11 2.1.010.
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My Notes

Find the slope of the tangent line to the graph of the function at the given point.

g(x) = 7 x + 7, (-6, 0)
6

7.–/1 pointsLarCalc11 2.1.021.
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My Notes

Find the derivative of the function by the limit process.f(x) = x2 + x ? 5

f ‘(x) =

8.–/1 pointsLarCalc11 2.1.025.
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My Notes

Find the derivative of the function by the limit process.f(x) =

7
x ? 8

f ‘(x) =

9.–/1 pointsLarCalc11 2.1.038.
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My Notes

Find an equation of the line that is tangent to the graph of f and parallel to the given line.

Function Line
f(x) = 2×2

4x ? y + 1 = 0

y =

10.–/1 pointsLarCalc11 2.2.013.
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My Notes

Use the rules of differentiation to find the derivative of the function.f(x) =

4 x
f ‘(x) =

11.–/1 pointsLarCalc11 2.2.017.
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My Notes

Use the rules of differentiation to find the derivative of the function.f(t) = 5t2 + 4t + 1

f ‘(t) =

12.–/1 pointsLarCalc11 2.2.026.
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My Notes

Use the rules of differentiation to find the derivative of the function.y = 3×4 + 8 sin x

y’ =

13.–/4 pointsLarCalc11 2.2.027.
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My Notes

Complete the table to find the derivative of the function.

Original Function Rewrite Differentiate Simplify
y =
3
5×4

x

14.–/1 pointsLarCalc11 2.2.035.
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My Notes

Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

Function Point
y = (8x + 2)2, (0, 4)

y'(0) =

15.–/1 pointsLarCalc11 2.2.041.
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My Notes

Find the derivative of the function.

g(t) = t2 ? 4
t3
g'(t) =

16.–/1 pointsLarCalc11 2.2.043.
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My Notes

Find the derivative of the function.

f(x) = x3 ? 3×2 + 9
x2
f ‘(x) =

17.–/1 pointsLarCalc11 2.2.049.
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My Notes

Find the derivative of the function.

f ‘(x) =

18.–/2 pointsLarCalc11 2.2.055.
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My Notes

Consider the given function and point.

f(x) = ?8×4 + 11×2 ? 3,(1, 0)

(a)

Find an equation of the tangent line to the graph of the function at the given point.

y =

(b)

Use a graphing utility to graph the function and its tangent line at the point. Use the tangent feature of the graphing utility to confirm your results.

19.–/7 pointsLarCalc11 2.2.095.
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My Notes

A silver dollar is dropped from the top of a building that is 1398 feet tall. Use the position function below for free-falling objects.s(t) = ?16t2 + v0t + s0

(a) Determine the position and velocity functions for the coin.

s(t) =
v(t) =

(b) Determine the average velocity on the interval [1, 2].
ft/s

(c) Find the instantaneous velocities when t = 1 second and t = 2 seconds.

v(1) = ft/s
v(2) = ft/s

(d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.)
t = s

(e) Find the velocity of the coin at impact. (Round your answer to three decimal places.)

ft/s

20.–/1 pointsLarCalc11 2.3.009.MI.
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My Notes

Use the Product Rule to differentiate the function.
f(x) = x3 cos(x)

f ‘(x) =

21.–/1 pointsLarCalc11 2.3.011.
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My Notes

Use the Quotient Rule to find the derivative of the function.f(x) =

x
x ? 4

f ‘(x) =

22.–/2 pointsLarCalc11 2.3.017.
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My Notes

Find f ‘(x)

and

f ‘(c).

Function Value of c
f(x) = (x3 + 2x)(3×4 + 3x ? 2) c = 0

f ‘(x) =

f ‘(c) =

23.–/2 pointsLarCalc11 2.3.022.
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My Notes

Find f ‘(x) and f ‘(c).

Function Value of c
f(x) =
sin x
x

c =

?
6

f ‘(x)

=

f ‘(c)

=

24.–/4 pointsLarCalc11 2.3.025.MI.SA.
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My Notes

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise

Find the derivative of the function without using the Quotient Rule.

15
13×4

25.–/1 pointsLarCalc11 2.3.029.
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My Notes

Find the derivative of the function.
f(x) =

4 ? 5x ? x2
x2 ? 6
f ‘(x) =

26.–/1 pointsLarCalc11 2.3.033.
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My Notes

Find the derivative of the function.f(x) =

9x ? 1

x
f ‘(x) =

27.
–/1 points
LarCalc11 2.3.041.
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My Notes
Question Part
Points
Submissions Used

Find the derivative of the trigonometric function.f(t) = t9 sin(t)

f ‘(t) =

28.
–/1 points
LarCalc11 2.3.043.
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My Notes
Question Part
Points
Submissions Used

Find the derivative of the trigonometric function.

f(t) = cos(t)
t
f ‘(t) =

29.
–/1 points
LarCalc11 2.3.049.
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My Notes
Question Part
Points
Submissions Used

Find the derivative of the trigonometric function.y =

5(1 ? sin(x))
2 cos(x)

y’ =